Problem: Rewrite as a simplified fraction. ${2.74\overline{3} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2743.3333...\\ 100x &= 274.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2469}$ ${x = \dfrac{2469}{900}} $ ${x = \dfrac{823}{300}} \text{or} {2 \dfrac{223}{300}}$